A conventional faucet structure is shown in FIG. 9, including a water outlet head (30) and a switch unit (40), wherein the water outlet head (30) has a water output end (31) that has a through hole (32) on top and a valve opening (33) near the water outlet end (31), and the valve opening (33) extends to have a connecting section (34). The switch unit (40) has a control rod (41), a valve piece (42) and a sealing element (43). The control rod (41) pokes through the through hole (32) of the water outlet head (30), and the valve piece (42) is at the bottom section. The valve piece (42) tightly touches the valve opening (33) of the water outlet head (30), and recessedly forms a position slot (421) on the side. The position slot (421) is provided for the sealing element (43) to engage with, and a recessed cut (431) is formed on one side of the sealing element (43), and the recessed cut (431) forms an attaching end (432) that is disposed against the opening surface of the position slot (421) of the valve piece (42). Also, a slanting end (433) is formed inside the attaching end (432) and a connecting hole (434) is formed and through the opening surface of the recessed cut (431). When in use, the connecting section (34) of the water outlet head (30) is connected to the water supply and when the user lifts the control rod (41), the valve piece (42) close the valve opening (33), so that the water can be directed to the showerhead. When the water supply is off, the pressure in the water outlet head (30) is reduced and the valve piece (42) detaches from the valve opening (33) of the water outlet head (30) due to gravity, so that the position of the water outlet head (30) can be automatically switched to avoid unexpected water output when using it next time. The conventional structure is disadvantageous because (a) when the water supply is off, the valve piece (42) is affected by residual water pressure inside the water outlet head (30), so the automatic switch is not complete and water may come out from the showerhead unexpectedly; (b) when valve piece (42) switches, the sealing element (43) can be easily affected by the edge of the valve opening (33) to increase the gap (B) between the periphery of the sealing element (43) and the position slot. Also, when water flows into the sealing element (43) from the connecting hole (434) to hold the recessed cut (431) of the sealing element (43) open, the attaching end (432) of the recessed cut (431) has a slanting end (433) inside so the attaching end (432) can be pushed and lifted by water flow to leak from the gap (B). Therefore, there remains a need for a new and improved control structure of the faucet to overcome abovementioned disadvantages.